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Concept

Map (mathematics)

Map (mathematics)
Function_color_example_3.gif: Wvbailey. The original uploader was Wvbailey at English Wikipedia. derivative work: Zerodamage · CC BY-SA 3.0 · source

Overview

In mathematics, a map or mapping is a function in its general sense. These terms may have originated as from the process of making a geographical map: mapping the Earth surface to a sheet of paper.

The term map may be used to distinguish some special types of functions, such as homomorphisms. For example, a linear map is a homomorphism of vector spaces, while the term linear function may have this meaning or it may mean a linear polynomial. In category theory, a map may refer to a morphism. The term transformation can be used interchangeably, but transformation often refers to a function from a set to itself. There are also a few less common uses in logic and graph theory.

Overview adapted from Wikipedia (CC BY-SA 4.0; see the article history for authors).

Possible passages

Found by search and not yet checked by a person; they may only mention the idea in passing.

  1. Of what use is this formulated statement of experience? Of what use is the map? Well, we may first tell what the map is not. The map is not a substitute for a personal experience. The map does not take the place of an actual journey.

    John Dewey, The Child and the Curriculum

    Names Map several times; states what Map is.

    Read the chapter · Open in the reader

  2. The eastern and western boundaries of our map are continents, and they are rising areas: the central spaces of the great Indian and Pacific Oceans, are mostly subsiding; between them, north of Australia, lies the most broken land on the globe, and there the rising parts are surrounded and penetrated by areas of subsidence,[39] so that the prevailing movements now in progress, seem to accord with the actual states of…

    Charles Darwin, Coral Reefs

    States what Map is; names Map several times.

    Read the chapter · Open in the reader

  3. Any such select set is called the set of postulates, or premises, from which the reasoning proceeds. The reasoning is nothing else than the exhibition of the whole pattern of general conditions involved in the pattern derived from the selected postulates.

    Alfred North Whitehead, Science and the modern world

    States what Map is.

    Read the chapter · Open in the reader

Related ideas

Place in the tradition

Part of Outline of logic.

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